Holographic Dual to Conical Defects III: Improved Image Method

TL;DR

This paper introduces an improved geodesic image method for calculating two-point Lorentzian correlators in AdS spacetimes with point particles, extending applicability to arbitrary time intervals and complex backgrounds.

Contribution

It proposes a novel geodesic image technique that works for general Lorentzian backgrounds with point particles, overcoming limitations of previous methods.

Findings

Consistent with existing analytic continuation and quasigeodesic approaches

Applicable to holographic entanglement entropy calculations

Handles multiple particles in AdS3 environments

Abstract

The geodesics prescription in holographic approach in Lorentzian signature is valid only for geodesics which connect spacelike-separated points at the boundary, since there are no timelike geodesics which reach the boundary. There is also no straightforward analytic Euclidean continuation for a general background, such as e. g. moving particle in AdS. We propose an improved geodesic image method for two-point Lorentzian correlators which is valid for arbitrary time intervals in case of the bulk spacetime deformed by point particles. We illustrate that our prescription is consistent with the case when the analytic continuation exists and with the quasigeodesics prescription used in previous work. We also discuss some other applications of the improved image method, such as holographic entanglement entropy and multiple particles in AdS3.